6.4.6 Sinusoidal Projection (-Ji -JI)

The sinusoidal projection is one of the oldest known projections, is equal-area, and has been used since the mid-16th century. It has also been called the ``Equal-area Mercator'' projection. The central meridian is a straight line; all other meridians are sinusoidal curves. Parallels are all equally spaced straight lines, with scale being true along all parallels (and central meridian). To use it, you need to select:

$\bullet$

The central meridian

$\bullet$

Scale along equator in inch/degree or 1:xxxxx (-Ji), or map width (-JI)

A simple world map using the sinusoidal projection is therefore obtained by

pscoast -Rd -JI0/4.5i -Bg30/g15 -Dc -A10000 -Ggray -P > GMT_sinusoidal.ps

Figure 6.27: World map using the Sinusoidal projection.

To reduce distortion of shape the interrupted sinusoidal projection was introduced in 1927. Here, three symmetrical segments are used to cover the entire world. Traditionally, the interruptions are at 160$^{o}$W, 20$^{o}$W, and 60$^{o}$E. To make the interrupted map we must call pscoast for each segment and superpose the results. To produce an interrupted world map (with the traditional boundaries just mentioned) that is 5.04 inches wide we use the scale 5.04/360$^{o}$ = 0.014 and offset the subsequent plots horizontally by their widths (140$^{o}$$\cdot$0.014 and 80$^{o}$ $\cdot$0.014):

pscoast -R200/340/-90/90 -Ji270/0.014i -Bg30/g15 -A10000 -Dc -Gblack -K -P > GMT_sinus_int.ps
pscoast -R-20/60/-90/90 -Ji20/0.014i -Bg30/g15 -Dc -A10000 -Gblack -X1.96i -O -K >> GMT_sinus_int.ps
pscoast -R60/200/-90/90 -Ji130/0.014i -Bg30/g15 -Dc -A10000 -Gblack -X1.12i -O >> GMT_sinus_int.ps

Figure 6.28: World map using the Interrupted Sinusoidal projection.

The usefulness of the interrupted sinusoidal projection is basically limited to display of global, discontinuous data distributions like hydrocarbon and mineral resources, etc.